CALCULATION OF THE ANGULAR RADIANCE DISTRIBUTION FOR A COUPLED ATMOSPHERE AND CANOPY

The radiative transfer equations for a coupled atmosphere and canopy a re solved numerically by an improved Gauss-Seidel iteration algorithm. The radiation field is decomposed into three components: unscattered sunlight, single scattering, and multiple scattering radiance for whic h the corresponding equations and boundary conditions are set up and t heir analytical or iterational solutions are explicitly derived. The c lassic Gauss-Seidel algorithm has been widely applied in atmospheric r esearch. This is its first application for calculating the multiple sc attering radiance of a coupled atmosphere and canopy. This algorithm e nables us to obtain the internal radiation field as well as radiances at boundaries. Any form of bidirectional reflectance distribution func tion (BRDF) as a boundary condition can be easily incorporated into th e iteration procedure. The hotspot effect of the canopy is accommodate d by means of the modification of the extinction coefficients of upwar d single scattering radiation and unscattered sunlight using the formu lation of Nilson and Kuusk Th reduce the computation for the case of l arge optical thickness, an improved iteration formula is derived to sp eed convergence. The upwelling radiances have been evaluated for diffe rent atmospheric conditions, leaf area index (LAI), leaf angle distrib ution (LAD), leaf size and so on. The formulation presented in this pa per is also well suited to analyze the relative magnitude of multiple scattering radiance and single scattering radiance in both the visible and near infrared regions.